1. Field of the Invention
The present invention relates to a direction finder which is capable of accurately finding the directions of radio waves propagating from a plural number of radio sources.
2. Description of the Prior Art
The scheme of a prior direction finder is shown in FIG. 5. The direction finder shown is designed on the basis of the descriptions by Ralph O. Schmidt in his paper "Multiple Emitter Location and Signal Parameter Estimation", IEEE Transaction on Antenna and Propagation, Vol. AP-34, No. 3, March 1986.
An application of the direction finder is illustrated in FIG. 6.
In FIG. 5, reference numeral 2 is an antenna platform on which a plural number of antennas directed in the same direction are arrayed and mounted thereon; 3 is a signal processor C 3 for processing signals in a conventional manner; 4 is a rotation driver for rotating the an antenna platform 2; 5-1 to 5-M are antennas of the same specifications for receiving the radio waves from radio sources; 6-1 to 6-m are receivers having the same specifications for receiving the radio wave signals from the antennas 5-1 to 5-M and for amplifying and frequency-converting the radio wave signals; 7 is a covariance matrix computing means which simultaneously samples the output signals of the M number of receivers and snapshoots the results plural times, and computes a covariance matrix on the output signals; 8 is an eigenvalue/eigenvector computing means for computing eigenvalues and eigenvectors from the covariance matrix; 9 is a noise-subspace projection length computing means for projecting mode vectors to a noise subspace defined by the eigenvalues and the eigenvectors and for computing the projection length of each mode vector; 10 is a minimum projection-length computing means which scans each imaginary radio source in the subspace, and computes an azimuthal angle and an elevation angle of the imaginary radio source when the projection length output from the noise-subspace projection length computing means 9 is locally minimized; 11 is a mode vector computing means for computing a predicted mode vector predicted on the basis of the imaginary wave source; and 12 is a control unit for issuing predetermined rotation angle commands to the rotation driver 4 and the mode vector computing means 11.
In FIG. 6, reference numeral 1 designates artificial satellites as radio sources.
The operation of the direction finder thus configured will be described.
It is assumed that the number D of the artificial satellites 1 is smaller than the number M of the antennas 5 (D&lt;M), and that the signals emitted from the radio sources are not correlated with one another. The output signals of the M number of the antennas 5 are input to the receivers 6 where those are amplified and frequency-converted.
The output signals of the receivers 6 are input to the covariance matrix computing means 7. Assuming that the output signals of the receivers 6 are S1, S2, . . . , SM, then a signal vector is given by the following expression 1. ##EQU1##
The covariance matrix computing means 7 snapshoots the output signals from the receivers 6 P times, and computes a covariance matrix on the output signals, which is given by the following expression 2. ##EQU2##
The covariance matrix of expression 2 constitutes an output signal of the covariance matrix computing means 7. In the expression, * represents conjugate or Hermitian conjugate.
The eigenvalue/eigenvector computing means 8 computes an M number of eigenvalues from the covariance matrix, then computes eigenvectors corresponding the eigenvalues, and outputs the results to the noise-subspace projection length computing means 9. Assuming that the eigenvalues are .lambda.1 to .lambda.M and the eigenvectors are X1 to X.sub.M, we have the following expression 3 as an output signal of the eigenvalue/eigenvector computing means 8 from the expression 2. ##EQU3##
As seen, the covariance matrix takes the form of a positive definite matrix. In the positive definite matrix, the eigen values are all larger than zero (0). It is assumed that the noise quantities or figures of the receivers 6 are all equal to one another, and a standard deviation of the noise distribution is .sigma.. Then, the following relation holds among the eigenvalues on the already-stated assumption that the D number of signals are not correlated. EQU .lambda..sub.1 .gtoreq..lambda..sub.2 .gtoreq.. . . .lambda..sub.D .gtoreq..lambda..sub.D+1 .gtoreq.=. . . =.lambda..sub.M =.sigma..sup.2 ( 4)
A signal subspace defined by the eigenvectors X.sub.1 to X.sub.D, which correspond to the eigenvalues .lambda..sub.1 to .lambda..sub.D, is orthogonally complementary to a noise subspace defined by the eigenvectors X.sub.D+1 to X.sub.M, which correspond to the eigenvalues .lambda..sub.D+1 to .lambda..sub.M.
In a case where an M number of antennas 5 are arrayed and radio sources are located in the directions deviated at angles from the standard or reference direction, data of the M number of antenna output signals, i.e., mode vectors, are stored in the mode vector computing means 11. Usually, those angles are within a predetermined range of angles.
The mode vector computing means 11 computes and generates mode vectors within a range of angles at and near a position defined by a direction command containing an azimuth and an elevation, which is received from the control unit 12. The direction command is also sent to the instantaneous-field-of-view invariable rotation driver 14, from the control unit 12. The rotation driver 14 responds to the direction command, and turns the antenna platform 2 in the direction specified by the direction command.
Accordingly, the mode vector computing means 11 computes and generates a mode vector defined by an azimuth a and an elevation .beta., and sends the result to the noise-subspace projection length computing means 9. The noise-subspace projection length computing means 9 projects the mode vector to a noise subspace defined by the eigenvalues and the eigenvectors, which have been input thereto. The noise-subspace projection length computing means 9 produces a projection length given by an expression 5. ##EQU4## where a(.alpha., .beta.): mode vector.
The minimum projection-length computing means 10, while handling the projection length of the mode vector a(.alpha., .beta.) as the function of .alpha. and .beta., computes D sets of the values of .alpha. and .beta. which locally minimize the projection length; (.alpha.1, .beta.1), (.alpha.2, .beta.2), . . . , (.alpha.D, .beta.D).
Those values (.alpha.1, .beta.1), (.alpha.2, .beta.2), . . . , (.alpha.D, .beta.D) are estimated angular values defining the directions in which the D number of radio sources are located.
The prior direction finder thus constructed suffers from the following problem. An attempt to increase the antenna aperture in order to improve the S/N (signal/noise) ratio of the output signal of each antenna, brings about an increase of the distance between the adjacent antennas. The result is that grating lobes is produced, and an imaginary radio source appears in the direction in which radio sources cannot be located.